Think of it as Windows++ [...] Cygwin = Windows + 0.75*unix

How can you make such claims and still claim that Cygwin is Windows? Your math doesn't add up.

Furthermore, Cygwin doesn't just add to Windows. It's different from Windows in many respects. You've already pointed out it treats line endings differently, and that's just one difference. However you want to classify Cygwin, saying it's Windows is a lie.

At its heart, cygwin really isn't an emulator, it's a compatibility DLL that you can link your programs against to gain some unix capabilities in your programs.

Yes, it's cool how the emulator autoloads.

It in no way prevents you from using the Windows API in your code

So? A lot of emulators allow you to break out of the box.

When you run an Atari game on it, the emulator treats the machine code as an interpreted language

Like Wine, it's an OS emulator, not a machine emulator or a combined machine and OS emulator. That it doesn't need to emulate the machine doesn't mean it's not an emulator.